<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<!--NewPage-->
<HTML>
<HEAD>
<META http-equiv="Content-Type" content="text/html; charset=UTF-8">
<TITLE>
RootsOfUnity (Commons Math 3.2 API)
</TITLE>


<LINK REL ="stylesheet" TYPE="text/css" HREF="../../../../../stylesheet.css" TITLE="Style">

<SCRIPT type="text/javascript">
function windowTitle()
{
    if (location.href.indexOf('is-external=true') == -1) {
        parent.document.title="RootsOfUnity (Commons Math 3.2 API)";
    }
}
</SCRIPT>
<NOSCRIPT>
</NOSCRIPT>

</HEAD>

<BODY BGCOLOR="white" onload="windowTitle();">
<HR>


<!-- ========= START OF TOP NAVBAR ======= -->
<A NAME="navbar_top"><!-- --></A>
<A HREF="#skip-navbar_top" title="Skip navigation links"></A>
<TABLE BORDER="0" WIDTH="100%" CELLPADDING="1" CELLSPACING="0" SUMMARY="">
<TR>
<TD COLSPAN=2 BGCOLOR="#EEEEFF" CLASS="NavBarCell1">
<A NAME="navbar_top_firstrow"><!-- --></A>
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="3" SUMMARY="">
  <TR ALIGN="center" VALIGN="top">
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../overview-summary.html"><FONT CLASS="NavBarFont1"><B>Overview</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="package-summary.html"><FONT CLASS="NavBarFont1"><B>Package</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#FFFFFF" CLASS="NavBarCell1Rev"> &nbsp;<FONT CLASS="NavBarFont1Rev"><B>Class</B></FONT>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="class-use/RootsOfUnity.html"><FONT CLASS="NavBarFont1"><B>Use</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="package-tree.html"><FONT CLASS="NavBarFont1"><B>Tree</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../deprecated-list.html"><FONT CLASS="NavBarFont1"><B>Deprecated</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../index-all.html"><FONT CLASS="NavBarFont1"><B>Index</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../help-doc.html"><FONT CLASS="NavBarFont1"><B>Help</B></FONT></A>&nbsp;</TD>
  </TR>
</TABLE>
</TD>
<TD ALIGN="right" VALIGN="top" ROWSPAN=3><EM>
</EM>
</TD>
</TR>

<TR>
<TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2">
&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex"><B>PREV CLASS</B></A>&nbsp;
&nbsp;NEXT CLASS</FONT></TD>
<TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2">
  <A HREF="../../../../../index.html?org/apache/commons/math3/complex/RootsOfUnity.html" target="_top"><B>FRAMES</B></A>  &nbsp;
&nbsp;<A HREF="RootsOfUnity.html" target="_top"><B>NO FRAMES</B></A>  &nbsp;
&nbsp;<SCRIPT type="text/javascript">
  <!--
  if(window==top) {
    document.writeln('<A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>');
  }
  //-->
</SCRIPT>
<NOSCRIPT>
  <A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>
</NOSCRIPT>


</FONT></TD>
</TR>
<TR>
<TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2">
  SUMMARY:&nbsp;NESTED&nbsp;|&nbsp;FIELD&nbsp;|&nbsp;<A HREF="#constructor_summary">CONSTR</A>&nbsp;|&nbsp;<A HREF="#method_summary">METHOD</A></FONT></TD>
<TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2">
DETAIL:&nbsp;FIELD&nbsp;|&nbsp;<A HREF="#constructor_detail">CONSTR</A>&nbsp;|&nbsp;<A HREF="#method_detail">METHOD</A></FONT></TD>
</TR>
</TABLE>
<A NAME="skip-navbar_top"></A>
<!-- ========= END OF TOP NAVBAR ========= -->

<HR>
<!-- ======== START OF CLASS DATA ======== -->
<H2>
<FONT SIZE="-1">
org.apache.commons.math3.complex</FONT>
<BR>
Class RootsOfUnity</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.complex.RootsOfUnity</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="http://download.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</A></DD>
</DL>
<HR>
<DL>
<DT><PRE>public class <B>RootsOfUnity</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A><DT>implements <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</A></DL>
</PRE>

<P>
A helper class for the computation and caching of the <code>n</code>-th roots of
 unity.
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>3.0</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: RootsOfUnity.java 1416643 2012-12-03 19:37:14Z tn $</DD>
<DT><B>See Also:</B><DD><A HREF="../../../../../serialized-form.html#org.apache.commons.math3.complex.RootsOfUnity">Serialized Form</A></DL>
<HR>

<P>

<!-- ======== CONSTRUCTOR SUMMARY ======== -->

<A NAME="constructor_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Constructor Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#RootsOfUnity()">RootsOfUnity</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build an engine for computing the <code>n</code>-th roots of unity.</TD>
</TR>
</TABLE>
&nbsp;
<!-- ========== METHOD SUMMARY =========== -->

<A NAME="method_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Method Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#computeRoots(int)">computeRoots</A></B>(int&nbsp;n)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 Computes the <code>n</code>-th roots of unity.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#getImaginary(int)">getImaginary</A></B>(int&nbsp;k)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the imaginary part of the <code>k</code>-th <code>n</code>-th root of unity.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#getNumberOfRoots()">getNumberOfRoots</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the number of roots of unity currently stored.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#getReal(int)">getReal</A></B>(int&nbsp;k)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the real part of the <code>k</code>-th <code>n</code>-th root of unity.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#isCounterClockWise()">isCounterClockWise</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns <code>true</code> if <A HREF="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#computeRoots(int)"><CODE>computeRoots(int)</CODE></A> was called with a
 positive value of its argument <code>n</code>.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
</TR>
</TABLE>
&nbsp;
<P>

<!-- ========= CONSTRUCTOR DETAIL ======== -->

<A NAME="constructor_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Constructor Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="RootsOfUnity()"><!-- --></A><H3>
RootsOfUnity</H3>
<PRE>
public <B>RootsOfUnity</B>()</PRE>
<DL>
<DD>Build an engine for computing the <code>n</code>-th roots of unity.
<P>
</DL>

<!-- ============ METHOD DETAIL ========== -->

<A NAME="method_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Method Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="isCounterClockWise()"><!-- --></A><H3>
isCounterClockWise</H3>
<PRE>
public boolean <B>isCounterClockWise</B>()
                           throws <A HREF="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</A></PRE>
<DL>
<DD>Returns <code>true</code> if <A HREF="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#computeRoots(int)"><CODE>computeRoots(int)</CODE></A> was called with a
 positive value of its argument <code>n</code>. If <code>true</code>, then
 counter-clockwise ordering of the roots of unity should be used.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD><code>true</code> if the roots of unity are stored in
 counter-clockwise order
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</A></CODE> - if no roots of unity have been computed
 yet</DL>
</DD>
</DL>
<HR>

<A NAME="computeRoots(int)"><!-- --></A><H3>
computeRoots</H3>
<PRE>
public void <B>computeRoots</B>(int&nbsp;n)
                  throws <A HREF="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</A></PRE>
<DL>
<DD><p>
 Computes the <code>n</code>-th roots of unity. The roots are stored in
 <code>omega[]</code>, such that <code>omega[k] = w ^ k</code>, where
 <code>k = 0, ..., n - 1</code>, <code>w = exp(2 * pi * i / n)</code> and
 <code>i = sqrt(-1)</code>.
 </p>
 <p>
 Note that <code>n</code> can be positive of negative
 </p>
 <ul>
 <li><code>abs(n)</code> is always the number of roots of unity.</li>
 <li>If <code>n &gt; 0</code>, then the roots are stored in counter-clockwise order.</li>
 <li>If <code>n &lt; 0</code>, then the roots are stored in clockwise order.</p>
 </ul>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>n</CODE> - the (signed) number of roots of unity to be computed
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</A></CODE> - if <code>n = 0</code></DL>
</DD>
</DL>
<HR>

<A NAME="getReal(int)"><!-- --></A><H3>
getReal</H3>
<PRE>
public double <B>getReal</B>(int&nbsp;k)
               throws <A HREF="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</A>,
                      <A HREF="../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</A></PRE>
<DL>
<DD>Get the real part of the <code>k</code>-th <code>n</code>-th root of unity.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>k</CODE> - index of the <code>n</code>-th root of unity
<DT><B>Returns:</B><DD>real part of the <code>k</code>-th <code>n</code>-th root of unity
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</A></CODE> - if no roots of unity have been
 computed yet
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</A></CODE> - if <code>k</code> is out of range</DL>
</DD>
</DL>
<HR>

<A NAME="getImaginary(int)"><!-- --></A><H3>
getImaginary</H3>
<PRE>
public double <B>getImaginary</B>(int&nbsp;k)
                    throws <A HREF="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</A>,
                           <A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></PRE>
<DL>
<DD>Get the imaginary part of the <code>k</code>-th <code>n</code>-th root of unity.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>k</CODE> - index of the <code>n</code>-th root of unity
<DT><B>Returns:</B><DD>imaginary part of the <code>k</code>-th <code>n</code>-th root of unity
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</A></CODE> - if no roots of unity have been
 computed yet
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></CODE> - if <code>k</code> is out of range</DL>
</DD>
</DL>
<HR>

<A NAME="getNumberOfRoots()"><!-- --></A><H3>
getNumberOfRoots</H3>
<PRE>
public int <B>getNumberOfRoots</B>()</PRE>
<DL>
<DD>Returns the number of roots of unity currently stored. If
 <A HREF="../../../../../org/apache/commons/math3/complex/RootsOfUnity.html#computeRoots(int)"><CODE>computeRoots(int)</CODE></A> was called with <code>n</code>, then this method
 returns <code>abs(n)</code>. If no roots of unity have been computed yet, this
 method returns 0.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the number of roots of unity currently stored</DL>
</DD>
</DL>
<!-- ========= END OF CLASS DATA ========= -->
<HR>


<!-- ======= START OF BOTTOM NAVBAR ====== -->
<A NAME="navbar_bottom"><!-- --></A>
<A HREF="#skip-navbar_bottom" title="Skip navigation links"></A>
<TABLE BORDER="0" WIDTH="100%" CELLPADDING="1" CELLSPACING="0" SUMMARY="">
<TR>
<TD COLSPAN=2 BGCOLOR="#EEEEFF" CLASS="NavBarCell1">
<A NAME="navbar_bottom_firstrow"><!-- --></A>
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="3" SUMMARY="">
  <TR ALIGN="center" VALIGN="top">
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../overview-summary.html"><FONT CLASS="NavBarFont1"><B>Overview</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="package-summary.html"><FONT CLASS="NavBarFont1"><B>Package</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#FFFFFF" CLASS="NavBarCell1Rev"> &nbsp;<FONT CLASS="NavBarFont1Rev"><B>Class</B></FONT>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="class-use/RootsOfUnity.html"><FONT CLASS="NavBarFont1"><B>Use</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="package-tree.html"><FONT CLASS="NavBarFont1"><B>Tree</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../deprecated-list.html"><FONT CLASS="NavBarFont1"><B>Deprecated</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../index-all.html"><FONT CLASS="NavBarFont1"><B>Index</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../help-doc.html"><FONT CLASS="NavBarFont1"><B>Help</B></FONT></A>&nbsp;</TD>
  </TR>
</TABLE>
</TD>
<TD ALIGN="right" VALIGN="top" ROWSPAN=3><EM>
</EM>
</TD>
</TR>

<TR>
<TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2">
&nbsp;<A HREF="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex"><B>PREV CLASS</B></A>&nbsp;
&nbsp;NEXT CLASS</FONT></TD>
<TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2">
  <A HREF="../../../../../index.html?org/apache/commons/math3/complex/RootsOfUnity.html" target="_top"><B>FRAMES</B></A>  &nbsp;
&nbsp;<A HREF="RootsOfUnity.html" target="_top"><B>NO FRAMES</B></A>  &nbsp;
&nbsp;<SCRIPT type="text/javascript">
  <!--
  if(window==top) {
    document.writeln('<A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>');
  }
  //-->
</SCRIPT>
<NOSCRIPT>
  <A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>
</NOSCRIPT>


</FONT></TD>
</TR>
<TR>
<TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2">
  SUMMARY:&nbsp;NESTED&nbsp;|&nbsp;FIELD&nbsp;|&nbsp;<A HREF="#constructor_summary">CONSTR</A>&nbsp;|&nbsp;<A HREF="#method_summary">METHOD</A></FONT></TD>
<TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2">
DETAIL:&nbsp;FIELD&nbsp;|&nbsp;<A HREF="#constructor_detail">CONSTR</A>&nbsp;|&nbsp;<A HREF="#method_detail">METHOD</A></FONT></TD>
</TR>
</TABLE>
<A NAME="skip-navbar_bottom"></A>
<!-- ======== END OF BOTTOM NAVBAR ======= -->

<HR>
Copyright &#169; 2003-2013 <a href="http://www.apache.org/">The Apache Software Foundation</a>. All Rights Reserved.
</BODY>
</HTML>
